Arandjelovic et al [1]} introduced a trainable generalized VLAD layer, named NetVLAD, which is pluggable into any CNN architecture. Local image descriptors clusters hard-assignments \(a_k(x_{i})\)  in the original VLAD are the source of discontinuities and prevent differentiability in the learning procedure. The authors replaced them with soft-assignment to make it amenable to backpropagation:
\({\alpha }_{k}(x_{i}) = \frac{e^{-\alpha \Vert x_{i}-c_{k} \Vert ^{2}}}{\sum _{j=1}^{K}e^{-\alpha \Vert x_{i}-c_{j} \Vert ^{2}}}\) 
